A. V. Kryazhimskii

On combination of the processes of reconstruction and guaranteeing control

Consideration was given to the problem of controlling a system of ordinary differential equations under incomplete information about the phase states. Given was an algorithm to solve it on the basis of a combination of the “real-time” reconstruction processes and feedback control.

On identification of nonobservable contamination inputs

The problem considered is that of estimating time-varying pollution inputs to a environmental system when no direct measurements are possible. Assuming that the rate of input of pollutants can be observed indirectly and that its relation to the observations is known, the problem is a model-inversion problem. However, the relation is generally not unique, i.e. more than one set of input behaviour may be consistent with it and the observations. The paper considers two approaches to obtaining information on the input: the reconstructibility approach and the guaranteed interval approach. The reconstructibility approach leads to reliable but restricted information. The result of the reconstructibility approach is an input performance index (a function). The guaranteed interval approach is an extension of the reconstructibility approach and considers unimprovable lower and upper bounds on an input performance index. The paper presents an algorithm for the guaranteed interval approach.

N.N. Krasovskii's extremal shift method and problems of boundary control

For the boundary-controlled dynamic system obeying a parabolic differential equation with the Neumann boundary condition, the problems of following the reference motion, following the reference control, and guaranteed control (at domination of the controller resource) were solved on the basis of the N.N. Krasovskii method of extremal shift from the theory of positional differential games.

Constraint Aggregation Principle in the Problem of Optimal Control of Distributed Parameter Systems

Abstract A problem of optimal control for a linear dynamical system in a Hilbert space is discussed. Control variables are subject to mixed linear constraints. To construct a finite-step iteration procedure that stop at an approximate solution having a prescribed accuracy, a semigroup representation of trajectories is used. Some applications to dynamical systems governed by parabolic and functional-differential equations with time lags are presented.

On dynamical regularization under random noise

We consider the problem of constructing a robust dynamic approximation of a timevarying input to a control system from the results of inaccurate observation of the states of the system. In contrast to the earlier studied cases in which the observation errors are assumed to be small in the metric sense, the errors in the present case are allowed to take, generally, large values and are subject to a certain probability distribution. The observation errors occurring at different instants are supposed to be statistically independent. Under the assumption that the expected values of the observation errors are small, we construct a dynamical algorithm for approximating the normal (minimal in the sense of the mean-square norm) input; the algorithm ensures an arbitrarily high level of the mean-square approximation accuracy with an arbitrarily high probability.

On the Design of an Optimal Stable Observer-Controller

Abstract For a control system acting under dynamical disturbances, the method of guided models worked out in Krasovskii and Subbotin, 1974, is modified for the case where a part of state coordinates is observed. It allows to design a control law making the systems motions to lie close to those generated by an arbitrary feedback using all state coordinates. The approximation is stable with respect to small observation perturbations. As an example, the problem of guiding a double-link pendulum along a prescribed trajectory through observations of one link is considered.